发展方程的时间离散化惯性流形－Ⅰ

TIME DISCRETIZATION INERTIAL MANIFOLDS FOR EVOLUTION EQUATION-Ⅰ

讨论了一类耗散发展方程时间离散化之后惯性流形的存在性，证明了如果时间步长充分小，且主算子Ａ满足一个谱间隔条件，则所讨论的发展方程的一个简单差分格式存在一个惯性流形从，与ＤｅｍｅｎｇｅｌＦ．的研究结果相比较，不仅简化了存在性证明，而且所建立的理论适用于更一般的非线性项，更进一步，在所建立的框架下，可以构造一个惯性流形序列｛ＭｈＭ｝，在某种意义下，当Ｍ→∞时，从ＭｈＭ→Ｍｈ，当ｈ趋于零时Ｍｈ的收敛性以及理论应用将在第Ⅱ部分讨论。

In this paper the existence of inertial manifolds under time discretization for a class ofnonlinear evolution equation is discussed. It shows that if the time step h is sufficiently smalland the spectral gap condition for principle A is satisfied, then a simply difference scheme,corresponding to the evolution equation under discussion, possesses an inertial manifold Mh。This not only simplifies the proof of existence, but the theory can also be applied to moregeneral nonlinear terms, Moreover in this frame,it is possible to construct a sequence of in-ertial manifolds {MhM}which tends to Mh as M→∞。